Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1734 and 1738 the smallest integer that is 1506846 that is divisible by both numbers.
Least Common Multiple (LCM) of 1734 and 1738 is 1506846.
LCM(1734,1738) = 1506846
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 1734 and 1738. First we will calculate the prime factors of 1734 and 1738.
Prime Factorization of 1734
2 | 1734 |
3 | 867 |
17 | 289 |
17 | 17 |
1 |
Prime factors of 1734 are 2, 3,17. Prime factorization of 1734 in exponential form is:
1734 = 21×31×172
Prime Factorization of 1738
2 | 1738 |
11 | 869 |
79 | 79 |
1 |
Prime factors of 1738 are 2, 11,79. Prime factorization of 1738 in exponential form is:
1738 = 21×111×791
Now multiplying the highest exponent prime factors to calculate the LCM of 1734 and 1738.
LCM(1734,1738) = 21×31×111×172×791
LCM(1734,1738) = 1506846
Factors of 1734
List of positive integer factors of 1734 that divides 1734 without a remainder.
1, 2, 3, 6, 17, 34, 51, 102, 289, 578, 867, 1734
Factors of 1738
List of positive integer factors of 1738 that divides 1738 without a remainder.
1, 2, 11, 22, 79, 158, 869, 1738
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1734 and 1738, than apply into the LCM equation.
GCF(1734,1738) = 2
LCM(1734,1738) = ( 1734 × 1738) / 2
LCM(1734,1738) = 3013692 / 2
LCM(1734,1738) = 1506846
(i) The LCM of 1738 and 1734 is associative
LCM of 1734 and 1738 = LCM of 1738 and 1734
1. What is the LCM of 1734 and 1738?
Answer: LCM of 1734 and 1738 is 1506846.
2. What are the Factors of 1734?
Answer: Factors of 1734 are 1, 2, 3, 6, 17, 34, 51, 102, 289, 578, 867, 1734. There are 12 integers that are factors of 1734. The greatest factor of 1734 is 1734.
3. What are the Factors of 1738?
Answer: Factors of 1738 are 1, 2, 11, 22, 79, 158, 869, 1738. There are 8 integers that are factors of 1738. The greatest factor of 1738 is 1738.
4. How to Find the LCM of 1734 and 1738?
Answer:
Least Common Multiple of 1734 and 1738 = 1506846
Step 1: Find the prime factorization of 1734
1734 = 2 x 3 x 17 x 17
Step 2: Find the prime factorization of 1738
1738 = 2 x 11 x 79
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1506846 = 2 x 3 x 11 x 17 x 17 x 79
Step 4: Therefore, the least common multiple of 1734 and 1738 is 1506846.